[MITgcm-support] MITgcm-support Digest, Vol 126, Issue 18 (momentum Budget)

Marco Reale reale.marco82 at gmail.com
Sun Dec 8 11:23:31 EST 2013


Dear Jean-Michel, Ryan , Dave and Martin

First of all I want to thank all of  you  for your useful suggestions and advice. they improved a lot my analysis and so I want to thank you for this. I applied your suggestions in the analysis of momentum budget.Following Jean Michel my balance has been computed like 

TOTUTEND/86400=- gravity * ( ETAN(i) - ETAN(i-1) ) / DXC   + Um_dPHdx+ Um_Advec   + Um_Diss + Um_Ext (is zero in my case)+ AB_gU…I’m currently running again the model to get Adams-bahsfort momentum tendency(despite in the first steps these terms look to be zero).

I fixed a point at level iz=12 , i=9, j=22  and i checked the value of TOTUTEND/86400 and  Ubalance=- gravity * ( ETAN(i) - ETAN(i-1) ) / DXC   + Um_dPHdx+ Um_Advec   + Um_Diss + Um_Ext (is zero in my case) for some timesteps (t) :


t=975
TOTUTEND/86400=1.6289e-09
Ubalance=1.4147e-09

t=1975

TOTUTEND/86400=1.5033e-09
Ubalance= 1.5004e-09

t=1875
TOTUTEND/86400=7.3823e-10
Ubalance=8.4034e-10


t=1775
TOTUTEND/86400=-6.6106e-10
Ubalance=-8.9608e-10

t=1990
TOTUTEND/86400=1.9254e-09
Ubalance=1.8055e-09


t=2000
TOTUTEND/86400=-2.0024e-09
Ubalance=-1.5492e-09

So in some time steps the agreement between my estimation and model’s estimation is good , in other cases no.In your opinion should these values be ok?  Where might it be the problem? I add as attachment the file data* that I used in my simulation.Is there anything wrong?

Cheers
Marco



Il giorno 07/dic/2013, alle ore 00:28, mitgcm-support-request at mitgcm.org ha scritto:

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> Today's Topics:
> 
>   1. Fwd:  input files for regional model (Jonny Williams)
>   2. Surface Deep Convection Tutorial (Stroman, Ashley)
>   3. Re: Balance of momentum (Jean-Michel Campin)
>   4. Re: Balance of momentum (Ryan Abernathey)
> 
> 
> ----------------------------------------------------------------------
> 
> Message: 1
> Date: Fri, 6 Dec 2013 17:32:30 +0000
> From: Jonny Williams <Jonny.Williams at bristol.ac.uk>
> To: "Menemenlis, Dimitris (3248)" <Dimitris.Menemenlis at jpl.nasa.gov>,
> 	MITgcm Support <mitgcm-support at mitgcm.org>
> Subject: [MITgcm-support] Fwd:  input files for regional model
> Message-ID:
> 	<CAA-NaP7e+icQAunLTH4k+apf50Rcgtx1WczSvex9Xe0t0WRQAQ at mail.gmail.com>
> Content-Type: text/plain; charset="iso-8859-1"
> 
> Hello again
> 
> I think I'm now at the stage of starting to run the regional model for my
> region of interest (as modified from the Arctic regional model)! Needless
> to say that my first go has not worked so here is a brief run through of
> what I've done so far to turn the Arctic regional model into my regional
> model
> 
> (1)  Modified the 'data' file to reflect the cartesian coordinate system
> now in use (copied from the 1D_ocean_ice_column verification experiment)...
> 
> # Gridding parameters
> &PARM04
> usingCartesianGrid=.TRUE.,
> dXspacing=185.2.,
> dYspacing=185.2.,
> delZ   = 10.00, 10.00, 10.00, 10.00, 10.00, 10.00, 10.00, 10.01,
> 10.03, 10.11, 10.32, 10.80, 11.76, 13.42, 16.04 , 19.82, 24.85,
> 31.10, 38.42, 46.50, 55.00, 63.50, 71.58, 78.90, 85.15, 90.18,
> 93.96, 96.58, 98.25, 99.25,100.01,101.33,104.56,111.33,122.83,
> 139.09,158.94,180.83,203.55,226.50,249.50,272.50,295.50,318.50,
> 341.50,364.50,387.50,410.50,433.50,456.50,
> &
> 
> 
> (2) Recompiled my executable (which worked) having already changed my
> SIZE.h file to what I believe to be a correct set of processor
> decomposition parameters
> 
> (3) Replaced all of the input '.dat' files with those which I have made
> from the global forcing dataset which I am using and repaced the relevant
> lines in, for example, data.exf and data.obcs.
> 
> This is basically the error I get (there is no extra information in the
> STDERR and STDOUT files)
> 
> "PGFIO-F-233/namelist read/unit=11/too many constants to initialize group
> item.
> File name = scratch1.0012    formatted, sequential access   record = 52
> *In source file exf_readparms.f, at line number 3657*
> [NID 02232] 2013-12-06 17:09:30 Apid 6359875: initiated application
> termination"
> 
> This refers to the following line...
> 
> "READ(  iUnit, nml = EXF_NML_04 )"
> 
> Which in turn refers to the following in data.exf...
> 
> "&EXF_NML_04
> precip_lon0       = -30.0D0,
> precip_lon_inc    = 0.1D0,
> precip_lat0       = -70.0D0,
> precip_lat_inc    = 800*0.1D0,
> precip_nlon       = 451,
> precip_nlat       = 801,"
> 
> I am trying to run at 0.1 degree resolution across a domain. Does this
> error mean that I am trying to run at an impossibly high resolution for a
> domain of this size?
> 
> Many thanks for any input once again and apologies for the long message.
> 
> Jonny
> 
> On 5 December 2013 18:32, Menemenlis, Dimitris (3248) <
> Dimitris.Menemenlis at jpl.nasa.gov> wrote:
> 
>> For lat/lon gid, you don't need any grid information files.
>> You specify everything in runtime parameter file "data"
>> See, for example, MITgcm/verification/lab_sea/input/data
>> 
>>  &PARM04
>> usingSphericalPolarGrid=.TRUE.,
>> delX=20*2.E0,
>> delY=16*2.E0,
>> delZ= 10., 10., 15., 20., 20., 25., 35., 50., 75.,
>>       100., 150., 200., 275., 350., 415., 450.,
>>       500., 500., 500., 500., 500., 500., 500.,
>> ygOrigin=46.,
>> xgOrigin=280.,
>> rSphere = 6371.D3,
>> &
>> 
>>  On Dec 5, 2013, at 10:24 AM, Jonny Williams wrote:
>> 
>> Hi there
>> 
>> I'm attempting to modify the Arctic regional model described here...
>> 
>> http://mitgcm.org/viewvc/MITgcm/MITgcm_contrib/arctic/cs_36km/readme.txt
>> http://ecco2.jpl.nasa.gov/data1/arctic/run_template2/README_arctic2.txt
>> 
>> My question is regarding the coordinate system. The Arctic model uses
>> "usingCurvilinearGrid=.TRUE.," in the data input file but I want to use a
>> regular latitude-longitude grid ("usingCartesianGrid=.TRUE.").
>> 
>> When I do this, do I also need all of the many other input files needed
>> (LATC.bin, LONC.bin, RA.bin, RAW.bin etc etc)?
>> 
>> If I don't need these files, then whereabouts do I specify information
>> regarding the grid system?
>> 
>> Many thanks :)
>> 
>> Jonny
>> 
>> 
>> 
>> _______________________________________________
>> MITgcm-support mailing list
>> MITgcm-support at mitgcm.org
>> http://mitgcm.org/mailman/listinfo/mitgcm-support
>> 
>> 
> 
> 
> -- 
> Dr Jonny Williams
> School of Geographical Sciences
> University of Bristol
> University Road
> BS8 1SS
> 
> +44 (0)117 3318352
> jonny.williams at bristol.ac.uk
> bit.ly/jonnywilliams
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> ------------------------------
> 
> Message: 2
> Date: Fri, 6 Dec 2013 22:22:09 +0000
> From: "Stroman, Ashley" <acs08g at my.fsu.edu>
> To: "mitgcm-support at mitgcm.org" <mitgcm-support at mitgcm.org>
> Subject: [MITgcm-support] Surface Deep Convection Tutorial
> Message-ID: <956C014B-2765-4A37-9CB8-BCD11A1A2A8D at my.fsu.edu>
> Content-Type: text/plain; charset="Windows-1252"
> 
> Hello.
> 
> I am trying to run the gendata script within the surface deep convection tutorial and I have two questions.
> 
> 1.) When I run the script in Matlab, I get an error output that says
> 
> BLAS loading error:
> mkl.so: failed to map segment from shared object: Cannot allocate
> memory
> 
> Error in gendata (line 41)
> xc=x'*ones(1,ny); yc=ones(nx,1)*y;
> 
> Is there a way to rewrite this part of the code so it won?t crash on me?
> 
> 2.) In the script, what is var calculating, and what what does the [1:1000) and /1000 come from?
> 
> Thanks.
> 
> Best,
> Ashley Stroman
> 
> 
> ------------------------------
> 
> Message: 3
> Date: Fri, 6 Dec 2013 17:48:15 -0500
> From: Jean-Michel Campin <jmc at ocean.mit.edu>
> To: mitgcm-support at mitgcm.org
> Subject: Re: [MITgcm-support] Balance of momentum
> Message-ID: <20131206224815.GA21051 at ocean.mit.edu>
> Content-Type: text/plain; charset=utf-8
> 
> Hi Marco, Dave, Martin and Ryan,
> 
> I would like to clarify few things regarding diagnostics of the
> horizontal momentum equation. I did not find very easy to follow
> the discussion started ~ a week ago (the subject has changed, not 
> always easy to distinguish quickly the answer from the quoting of 
> the original message and long lines are not easy to read from the 
> mitgcm-support archive web-site). But I hope this will not add more
> confusion.
> 
> The different horizontal momentum terms are split into different
> diagnostics, mainly to reflect the time-stepping options (forward
> in time = explicit / backward in time = implicit, and going
> through the Adams-Bashforth or not). A finer decomposition can
> be obtained with a 2nd (larger) set of diagnostics that are specific
> to the formulation used (flux-form or vector-invariant).
> 
> 1) the surface pressure horizontal gradient needs to be added.
> this was mentioned in the Emily's message that Martin (on Nov 28) pointed to:
> http://mitgcm.org/pipermail/mitgcm-support/2010-December/006921.html
> and it's needed whether or not the free-surface or the rigid-lid is used
> (in this later case, this is the pressure from the lid).
> 
> To Ryan: Having many diagnostics slows down the code (it's not 
> clear how much, but it does) and when some term can be easily and
> precisely recomputed from other diags, it's a matter of choice
> if we decide to add a diagnostics or not. 
> In this case, from a single 2-D diagnostics output (ETAN), one can 
> compute the horizontal gradient in both direction (DXC & DYC are 
> standard grid output); but we would need two 3-D diagnostics (to get it 
> properly masked) for the contribution at each level of the du/dt 
> and dv/dt equations. So, it's not very clear to me that these two
> 3-D diagnostics should be added (may be we can continue this discussion
> elsewhere). 
> 
> 2) Diagnostics Um_Advec and Um_Advec already contain the Coriolis
> term, unless one uses the CD-Scheme (and in this case, 
> Um_Cori and Vm_Cori needs to be added). 
> The main reason for this is that when using the vector-invariant form, 
> Coriolis term can be incorporated to the absolute vorticity (and then 
> treated with the advection), and in order to make the diagnostics more 
> similar between the 2 momentum formulations, the same convention was 
> retained also for the flux-form.
> Note that, for the same reasons, the metrics-terms are also part
> of Um_Advec and Um_Advec.
> 
> Now, here is where I get confused: In Emily's message, the CD-Scheme is 
> not used, but momentum budget is closed by adding Um_Cori to to Um_Advec ?
> 
> 3) Diagnostics Um_Diss and Vm_Diss contain all the explicit (forward
> in time) dissipation terms (horizontal viscosity, explicit vertical
> viscosity, side drag, bottom friction).
> If one uses implicit vertical viscosity (implicitViscosity=.TRUE.,),
> the vertical viscosity tendency needs to be added (as explained in
> Emily's message).
> 
> 4) forcing (diagnostics Um_Ext, Vm_Ext) and baroclinic pressure gradient
> (diagnostics Um_dPHdx and Vm_dPHdy) needs to be added separately.
> If filters are used (Shapiro, FFT), their contribution needs to be
> diagnosed separately (e.g., using SHAP_dU and SHAP_dV ).
> 
> 5) The Adams-Bashforth will alter the momentum budget (although over
> a long period, most cancel in time-averaging) and, depending on the 
> particular set of parameter (e.g., staggerTimeStep, forcing_In_AB, 
> momDissip_In_AB ) it's not always negligible. This AB effect can
> be diagnosed using the 2 diagnostics AB_gU and AB_gV (added 2 years ago).
> 
> So that the momentum budget for the U componentic can be diagnosed with:
> 
> [du/dt] = - gravity * ( ETAN(i) - ETAN(i-1) ) / DXC
>        + Um_dPHdx
>        + Um_Advec   (+ Um_Cori : but only if using CD-Scheme )
>        + Um_Diss    (+ Implicit vertical viscosity tendency)
>        + Um_Ext
>        + AB_gU
> 
> Some remarks:
> a) When using the flux-form formulation, the non-linear free-surface can introduce 
>   a small difference (rescaling) which is not currently diagnosed.
> b) the 3-D Coriolis ( in 2 Omega cos(Phi) between U and W) is not currently
>  diagnosed separately (and is not part of Um_Cori) but is part of
>  Um_Advec. Also using the quasiHydrostatic option might alter some of the 
>  diagnostics (e.g., what is described as the hydrostatic pressure is no 
>  longer strictly hydrostatic).
> c) when trying to do a budget over just 1 time-step, one needs to be aware 
>  of the precise time-discretisation of the the first term which is evaluated 
>  in the model as 
>   - gravity * {  implicSurfPress * (d.EtaN/dx)^n+1 
>                +(1-implicSurfPress)*(d.EtaN/dx)^n }
>  (using the default implicSurfPress=1 , it might be be easier to use 
>   snap-shot output Eta.[iter+1] to get EtaN^n+1 )
> 
> Cheers,
> Jean-Michel
> 
> On Thu, Dec 05, 2013 at 10:23:04AM +0000, David Munday wrote:
>> Hi Marco,
>> 
>> Um_HydroP isn't in my available_diagnostics, I can't find it anywhere in the documentation, and grepping the code turns up nothing. Is it the same as Um_dPHdx?
>> 
>> In general, I'd expect Um_Advec and Um_dPHdx to be similar in magnitude and of opposite sign, due to the dominance of geostrophic balance. Assuming Um_HydroP is Um_dPHdx by another name, then its magnitude is about right, but its sign is wrong (or Um_Advec's is). Taking the difference and adding Um_Diss gives me -4.3197E-9, so you're still missing a term.
>> 
>> Have you output every single Um_* diagnostic available, including the ones you think are zero, the implicit/explicit viscosity, and the gradient in SSH?
>> 
>> Best wishes,
>> 
>> Dave
>> 
>> 
>> On 4 Dec 2013, at 21:44, Marco Reale wrote:
>> 
>> Hi David,
>> 
>> and thanks a lot for your response: I followed your suggestion.
>> 
>> So finally  the equation will be :
>> 
>> TOTUTEND/86400=Um_Advec+Um_diss+Um_HydroP;
>> 
>> each of these members of the equation are 4D arrays : following a point to check the balance at t = 30, level=12, i=9, j=30 and I got the following results:
>> 
>> TOTUTEND/86400= -8.0561e-10
>> Um_Advec= 2.5398e-07
>> Um_diss= 7.7003e-09
>> Um_HydroP=2.4196e-07
>> 
>> the balance of this term is 5.0365e-07
>> 
>> 
>> So I have done something wrong: I?m working with rough data without taking into account volume of cells, etc.
>> 
>> Any suggestions?
>> 
>> Marco
>> 
>> 
> 
>> _______________________________________________
>> MITgcm-support mailing list
>> MITgcm-support at mitgcm.org
>> http://mitgcm.org/mailman/listinfo/mitgcm-support
> 
> 
> 
> 
> ------------------------------
> 
> Message: 4
> Date: Fri, 6 Dec 2013 18:28:15 -0500
> From: Ryan Abernathey <ryan.abernathey at gmail.com>
> To: "mitgcm-support at mitgcm.org" <mitgcm-support at mitgcm.org>
> Subject: Re: [MITgcm-support] Balance of momentum
> Message-ID: <A4DDE4B5-8675-4547-9833-241637BD01AC at gmail.com>
> Content-Type: text/plain;	charset=utf-8
> 
> JMC,
> What you say about the etan diagnostics makes perfect sense. I misunderstood the earlier email and thought there was some missing term that could only be output through hacking the code. I never had to do this in my momentum budgets, so I was kind of confused / worried. 
> -Ryan
> 
> Sent from my iPhone
> 
> On Dec 6, 2013, at 5:48 PM, Jean-Michel Campin <jmc at ocean.mit.edu> wrote:
> 
>> Hi Marco, Dave, Martin and Ryan,
>> 
>> I would like to clarify few things regarding diagnostics of the
>> horizontal momentum equation. I did not find very easy to follow
>> the discussion started ~ a week ago (the subject has changed, not 
>> always easy to distinguish quickly the answer from the quoting of 
>> the original message and long lines are not easy to read from the 
>> mitgcm-support archive web-site). But I hope this will not add more
>> confusion.
>> 
>> The different horizontal momentum terms are split into different
>> diagnostics, mainly to reflect the time-stepping options (forward
>> in time = explicit / backward in time = implicit, and going
>> through the Adams-Bashforth or not). A finer decomposition can
>> be obtained with a 2nd (larger) set of diagnostics that are specific
>> to the formulation used (flux-form or vector-invariant).
>> 
>> 1) the surface pressure horizontal gradient needs to be added.
>> this was mentioned in the Emily's message that Martin (on Nov 28) pointed to:
>> http://mitgcm.org/pipermail/mitgcm-support/2010-December/006921.html
>> and it's needed whether or not the free-surface or the rigid-lid is used
>> (in this later case, this is the pressure from the lid).
>> 
>> To Ryan: Having many diagnostics slows down the code (it's not 
>> clear how much, but it does) and when some term can be easily and
>> precisely recomputed from other diags, it's a matter of choice
>> if we decide to add a diagnostics or not. 
>> In this case, from a single 2-D diagnostics output (ETAN), one can 
>> compute the horizontal gradient in both direction (DXC & DYC are 
>> standard grid output); but we would need two 3-D diagnostics (to get it 
>> properly masked) for the contribution at each level of the du/dt 
>> and dv/dt equations. So, it's not very clear to me that these two
>> 3-D diagnostics should be added (may be we can continue this discussion
>> elsewhere). 
>> 
>> 2) Diagnostics Um_Advec and Um_Advec already contain the Coriolis
>> term, unless one uses the CD-Scheme (and in this case, 
>> Um_Cori and Vm_Cori needs to be added). 
>> The main reason for this is that when using the vector-invariant form, 
>> Coriolis term can be incorporated to the absolute vorticity (and then 
>> treated with the advection), and in order to make the diagnostics more 
>> similar between the 2 momentum formulations, the same convention was 
>> retained also for the flux-form.
>> Note that, for the same reasons, the metrics-terms are also part
>> of Um_Advec and Um_Advec.
>> 
>> Now, here is where I get confused: In Emily's message, the CD-Scheme is 
>> not used, but momentum budget is closed by adding Um_Cori to to Um_Advec ?
>> 
>> 3) Diagnostics Um_Diss and Vm_Diss contain all the explicit (forward
>> in time) dissipation terms (horizontal viscosity, explicit vertical
>> viscosity, side drag, bottom friction).
>> If one uses implicit vertical viscosity (implicitViscosity=.TRUE.,),
>> the vertical viscosity tendency needs to be added (as explained in
>> Emily's message).
>> 
>> 4) forcing (diagnostics Um_Ext, Vm_Ext) and baroclinic pressure gradient
>> (diagnostics Um_dPHdx and Vm_dPHdy) needs to be added separately.
>> If filters are used (Shapiro, FFT), their contribution needs to be
>> diagnosed separately (e.g., using SHAP_dU and SHAP_dV ).
>> 
>> 5) The Adams-Bashforth will alter the momentum budget (although over
>> a long period, most cancel in time-averaging) and, depending on the 
>> particular set of parameter (e.g., staggerTimeStep, forcing_In_AB, 
>> momDissip_In_AB ) it's not always negligible. This AB effect can
>> be diagnosed using the 2 diagnostics AB_gU and AB_gV (added 2 years ago).
>> 
>> So that the momentum budget for the U componentic can be diagnosed with:
>> 
>> [du/dt] = - gravity * ( ETAN(i) - ETAN(i-1) ) / DXC
>>       + Um_dPHdx
>>       + Um_Advec   (+ Um_Cori : but only if using CD-Scheme )
>>       + Um_Diss    (+ Implicit vertical viscosity tendency)
>>       + Um_Ext
>>       + AB_gU
>> 
>> Some remarks:
>> a) When using the flux-form formulation, the non-linear free-surface can introduce 
>>  a small difference (rescaling) which is not currently diagnosed.
>> b) the 3-D Coriolis ( in 2 Omega cos(Phi) between U and W) is not currently
>> diagnosed separately (and is not part of Um_Cori) but is part of
>> Um_Advec. Also using the quasiHydrostatic option might alter some of the 
>> diagnostics (e.g., what is described as the hydrostatic pressure is no 
>> longer strictly hydrostatic).
>> c) when trying to do a budget over just 1 time-step, one needs to be aware 
>> of the precise time-discretisation of the the first term which is evaluated 
>> in the model as 
>>  - gravity * {  implicSurfPress * (d.EtaN/dx)^n+1 
>>               +(1-implicSurfPress)*(d.EtaN/dx)^n }
>> (using the default implicSurfPress=1 , it might be be easier to use 
>>  snap-shot output Eta.[iter+1] to get EtaN^n+1 )
>> 
>> Cheers,
>> Jean-Michel
>> 
>> On Thu, Dec 05, 2013 at 10:23:04AM +0000, David Munday wrote:
>>> Hi Marco,
>>> 
>>> Um_HydroP isn't in my available_diagnostics, I can't find it anywhere in the documentation, and grepping the code turns up nothing. Is it the same as Um_dPHdx?
>>> 
>>> In general, I'd expect Um_Advec and Um_dPHdx to be similar in magnitude and of opposite sign, due to the dominance of geostrophic balance. Assuming Um_HydroP is Um_dPHdx by another name, then its magnitude is about right, but its sign is wrong (or Um_Advec's is). Taking the difference and adding Um_Diss gives me -4.3197E-9, so you're still missing a term.
>>> 
>>> Have you output every single Um_* diagnostic available, including the ones you think are zero, the implicit/explicit viscosity, and the gradient in SSH?
>>> 
>>> Best wishes,
>>> 
>>> Dave
>>> 
>>> 
>>> On 4 Dec 2013, at 21:44, Marco Reale wrote:
>>> 
>>> Hi David,
>>> 
>>> and thanks a lot for your response: I followed your suggestion.
>>> 
>>> So finally  the equation will be :
>>> 
>>> TOTUTEND/86400=Um_Advec+Um_diss+Um_HydroP;
>>> 
>>> each of these members of the equation are 4D arrays : following a point to check the balance at t = 30, level=12, i=9, j=30 and I got the following results:
>>> 
>>> TOTUTEND/86400= -8.0561e-10
>>> Um_Advec= 2.5398e-07
>>> Um_diss= 7.7003e-09
>>> Um_HydroP=2.4196e-07
>>> 
>>> the balance of this term is 5.0365e-07
>>> 
>>> 
>>> So I have done something wrong: I?m working with rough data without taking into account volume of cells, etc.
>>> 
>>> Any suggestions?
>>> 
>>> Marco
>> 
>>> _______________________________________________
>>> MITgcm-support mailing list
>>> MITgcm-support at mitgcm.org
>>> http://mitgcm.org/mailman/listinfo/mitgcm-support
>> 
>> 
>> _______________________________________________
>> MITgcm-support mailing list
>> MITgcm-support at mitgcm.org
>> http://mitgcm.org/mailman/listinfo/mitgcm-support
> 
> 
> 
> ------------------------------
> 
> _______________________________________________
> MITgcm-support mailing list
> MITgcm-support at mitgcm.org
> http://mitgcm.org/mailman/listinfo/mitgcm-support
> 
> 
> End of MITgcm-support Digest, Vol 126, Issue 18
> ***********************************************

***********************************
Marco Reale
ph.D student "Environmental and Industrial Fluid Mechanics"-XXVII cycle
University of Trieste-Department of Mathematics and Informatics
National Institute of Geophysics and Oceanography (OGS)
International Center for Theorethical Physics (ICTP)
Italian Geophysical Association (AGI)
Italian Meteorological Society (SMI)
European Geophysical Union (EGU)
web-page: http://phdfluidmechanics.appspot.com/stud.html?Reale
skype: mcreal82
phone number: +39 3270888069

***********************************

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